The Measurement of Time: Children's Construction of Transitivity,Unit Iteration,and Conservation of Speed

One hundred twenty children in kindergarten and grades 2, 4, and 6 were individually interviewed with five Piagetian tasks to determine the grade level at which most have constructed transitive reasoning, unit iteration, and the conservation of speed. The responses were categorized as “successful,”“unsuccessful,” or “transitional.” By combining the “successful” and “transitional” categories, it was found that the children reasoned transitively by second grade (70.0%) and demonstrated unit iteration and conservation of speed by sixth grade (70.0% and 83.3%, respectively). It was concluded that the construction of the logic necessary to make sense of the measurement of time is generally not complete before sixth grade.     

A biomimetic approach to the synthesis of a mycolic acid motif

A new method for the stereoselective synthesis of the (R,R)-β-hydroxy-α-alkyl fatty acid fragment of mycolic acids, via an asymmetric anti-aldol reaction is reported. The ‘mycolic acid motif’ fragment was prepared in three steps and >98% ee.     

Asymptotic zero distribution of a class of 3F2 hypergeometric functions

We study the asymptotic behavior of the zeros of certain families of ₃F₂ functions. Classical tools are used to analyse the asymptotic behavior of the zeros of the polynomial In addition, families of ₃F₂ functions that are connected in a formulaic sense with Gauss hypergeometric polynomials of the form and are investigated. Numerical evidence of the clustering o zeros on certain curves is generated by Mathematica.     

Copper‐Catalyzed Formation of α‐Alkoxycycloalkenones from N‐Tosylhydrazones

The combination of 20 mol % of copper iodide and lithium tert‐butoxide triggers the formation of a broad range of substituted, functionalized α‐alkoxy 2H‐naphthalenones from readily available N‐tosylhydrazones. The data suggests that this transformation occurs through cycloaddition of a copper carbenoid with an ester, followed by a Lewis acid‐catalyzed [1,2] alkyl shift of the in situ generated alkoxyepoxide intermediate.     

The crank moments weighted by the parity of cranks

In this note, we introduce the 2kth crank moment \(\mu _{2k}(-1,n)\) weighted by the parity of cranks and show that \((-1)^n \mu _{2k}(-1,n)>0\) for \(n\ge k \ge 0\). When \(k=0\), the inequality \((-1)^n \mu _{2k}(-1,n)>0\) reduces to Andrews and Lewis’s inequality \((-1)^n(M_e(n)-M_o(n))>0\) for \(n\ge 0\), where \(M_e(n)\) (resp. \(M_o(n)\)) denotes the number of partitions of n with even (resp. odd) crank. Several generating functions of \(\mu _{2k}(-1,n)\) are also studied in order to show the positivity of \((-1)^n\mu _{2k}(-1,n)\).     

Influence of patterned concave depth and surface curvature on anodization of titania nanotubes and alumina nanopores

Vertically aligned TiO(2) nanotube and Al(2)O(3) nanopore arrays have been obtained by pattern guided anodization with uniform concave depths. There are some studies about the effect of surface curvature on the growth of Al(2)O(3) nanopores. However, the surface curvature influence on the development of TiO(2) nanotubes is seldom studied. Moreover, there is no research about the effect of heterogeneous concave depths of the guiding patterns on the anodized TiO(2) nanotube and Al(2)O(3) nanopore characteristics, such as diameter, growth direction, and termination/bifurcation. In this study, focused ion beam lithography is used to create concave patterns with heterogeneous depths on flat surfaces and with uniform depths on curved surfaces. For the former, bending and bifurcation of nanotubes/nanopores are observed after the anodization. For the latter, bifurcation of a large tube into two smaller tubes occurs on concave surfaces, while termination of existing tubes occurs on convex surfaces. The growth direction of all TiO(2) nanotubes is perpendicular to the local surface and thus is different on different facets of the same Ti foil. At the edge of the Ti foil where two facets meet, the nanotube growth direction is bent, resulting in a large stress release that causes the formation of cracks.     

Moiré pattern nanopore and nanorod arrays by focused ion beam guided anodization and nanoimprint molding

Nanoporous anodic aluminum oxide has been intensively studied as templates in the fabrication of various nanomaterials. Most of the research focuses on highly ordered hexagonal nanopore arrangement with homogeneous area-specific pore density. Anodic aluminum oxide with alternating area-specific nanopore densities has seldom been addressed. In this study, focused ion beam patterned concave arrays created by overlapping two periodic patterns show the exceptional ability of guiding the subsequent anodization and fabricating porous anodic aluminum oxide with Moire? patterns, which have a wide range of interpore distances and area-specific pore densities. The periodicity of the Moire? patterns can be predicted by the interpore distance of the initial patterns and the rotation angle. The depth of the nanopores of these Moire? patterns is around 1 μm. Vertically aligned and high aspect ratio h-PDMS nanorod arrays with Moire? pattern arrangements have been successfully synthesized using the patterned porous anodic aluminum oxide as templates.     

The complex story of a simple Brønsted acid: unusual speciation of HBr in an ionic liquid medium

Crystalline solids, co-existing in equilibrium with the 3-methyl-1H-imidazolium bromohydrogenates(I) ionic liquid, have been characterised by X-ray diffraction analysis. The Br?nsted acidic, homo-conjugate [H(2)Br(3)](-) anions presented are discussed in terms of their structure and reactivity, in efforts to advance the understanding of Br?nsted acidity in ionic liquid media.